On persistence of invariant tori and a theorem by Nekhoroshev

TL;DR

This paper proves a theorem by Nekhoroshev that guarantees the persistence of certain invariant tori in Hamiltonian systems with multiple integrals of motion, under generalized nondegeneracy conditions.

Contribution

It provides a rigorous proof of Nekhoroshev's theorem extending the understanding of invariant tori in multi-integral Hamiltonian systems.

Findings

Invariant tori persist under specified conditions

Generalization of Poincaré's nondegeneracy condition

Enhanced stability results for Hamiltonian systems

Abstract

We give a proof of a theorem by N.N. Nekhoroshev concerning Hamiltonian systems with $n$ degrees of freedom and $s$ integrals of motion in involution, where $1 \le s \le n$. Such a theorem ensures persistence of $s$-dimensional invariant tori under suitable nondegeneracy conditions generalizing Poincar\'e's condition on the Floquet multipliers.